Answer:
{(-5, 7), (-4, -9), (–5, – 4), (2, -6)}
Step-by-step explanation:
In a function, no two points can have the same x-coordinates. In other words, all x-coordinates of the points must be different.
{(5, -6), (-1, - 2), (2, –9), (–8, -2)} : All x-coordinates are different: 5, -1, 2, -8. This is a function.
{(-5, 7), (-4, -9), (–5, – 4), (2, -6)} : Two x-coordinates are the same: -5, -5. This is not a function.
{(-4,2), (-2,8), (-1,6), (5,6)} : All x-coordinates are different: -4, -2, -1, 5. This is a function.
{(2,2), (-4,9), (9, -3), (-3, 2)}: All x-coordinates are different: 2, -4, 9, -3. This is a function.
here is an equation that is true for all values of x:5(x+2)=5x+10. Elena saw this equation and says she can tell 20(x+2)=4(5x+10)+31 is also true for any value of x. How can she tell? Explain your reasoning.
Elena is wrong, because the two sides of equation are not equal for all values of x
Step-by-step explanation:
An equation of x is true for all values of x when the left hand side
is equal to the right hand side
To prove that an equation is true for all values of x do that
Simplify the left hand side and the right hand sideSolve the equation to find x, you will find the x in the left hand side is equal to x in the right hand side, so they canceled each other, and the numerical terms in the two sides equal each other, that means the equation is true for any values of xLets check that with given equation 5(x + 2) = 5x + 10
∵ 5(x + 2) = 5x + 10
- Simplify the left hand side
∵ 5(x) + 5(2) = 5x + 10
∴ 5x + 10 = 5x + 10
- Subtract 5x from both sides
∴ 10 = 10
∵ L.H.S = R.H.S
∴ The equation is true for all values of x
Lets do that with Elena's equation
∵ 20(x + 2) = 4(5x + 10) + 31
- Simplify the two sides of the equation
∵ 20(x) + 20(2) = 4(5x) + 4(10) + 31
∴ 20x + 40 = 20x + 40 + 31
- Add like terms in the right hand side
∴ 20x + 40 = 20x + 71
- Subtract 20x from both sides
∴ 40 = 71 ⇒ and that not true
∵ L.H.S ≠ R.H.S
∴ The equation is not true for all values of x
Elena is wrong, because the two sides of equation are not equal for all values of x
Learn more:
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Elena took the original equation, multiplied both sides of it by 4 and added 31 to both sides. Because she did the same thing to both sides of the equation, it is equal to the original equation and therefore is true for all values of `x`.
Look at 4x + 5y - 12 - x + 3y . Have all of the like terms been combined? Explain in 1-2 sentences.
Answer:
no 4x and -x can be combined to form 3x, and 5y and 3y can be combned to form 8y. the correct equation should be 3x+8y-12
Step-by-step explanation:
find the value of x in this figure
x equals 47 degrees
Explanation:Remember you must provide full questions in order to get excellent and precise answers. However, I have attached a figure in order to set the problem in context. Here we have a triangle. The most basic definition for a triangle is a polygon with three edges and three vertices, but there is something that is very important for all triangles:
The internal angles of every triangle add up to 180 degrees.By knowing this, we can write:
[tex]x^{\circ}+95^{\circ}+38^{\circ}=180^{\circ} \\ \\ Isolating \ x: \\ \\ x^{\circ}=180^{\circ}-95^{\circ}-38^{\circ} \\ \\ x^{\circ}=47^{\circ} \\ \\ \\ Where: \\ \\ \boxed{x=47}[/tex]
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Anyone, please help. I’m a dimwit at math!
Answer: it should be "B. 73" if I'm incorrect sorry but it should be "B. 73"
Step-by-step explanation:
Evaluate the expression. ab if a = 6 and b = 7
Answer:
42
Step-by-step explanation:
ab is a x b
[tex]a \times b[/tex]
[tex]6 \times 7 = 42[/tex]
Answer:279,936
Step-by-step explanation:
i hope its helps
what value of n solves the equation 2n =1/8
A. -3
B. -4
C. 3
D. 4
Answer:
n = - 3
Step-by-step explanation:
We have to solve the equation [tex]2^{n} = \frac{1}{8}[/tex] for n.
Now, as the variable is in power, we will take a log on both sides.
So, [tex]2^{n} = \frac{1}{8}[/tex]
⇒ [tex]\log 2^{n} = \log \frac{1}{8}[/tex]
⇒ n log 2 = log 1 - log 8 {Since we know the property of logarithm [tex]\log a^{b} = b \log a[/tex] and [tex]\log \frac{a}{b} = \log a - \log b[/tex]}
⇒ n log 2 = - log 2³ { Since, log 1 = 0}
⇒ n log 2 = - 3 log 2
⇒ n = - 3 (Answer)
Kristina used synthetic division to divide the polynomial f(x) by x−2, as shown on the table. What is the value of f(2)? −14 −11 −2 −1 A synthetic division setup with respective columns containing the following numbers column 1 containing two as a divisor, column 2 containing negative 1, blank and negative 1, column 3 containing negative 5, negative 2, negative 7, and column 4 containing three, negative 14, negative 11.There is a line above the numbers negative 1, negative 7 and negative 11.
Answer:
-11
Step-by-step explanation:
The answer to the first one sould be -11
2x^3 +5x^2−x−6
Write 5x^2 as 4x^2 + x^2......and we have.....
2x^3 + 4x^2 + x^2 - x - 6
2x^2 ( x + 2) + ( x + 2)(x - 3)
(x + 2) [ 2x^2 + x - 3]
(x + 2) (2x +3) (x - 1)
x^3−4x^2−3x+18 = 0
Using some synthetic division, we have
3 [ 1 - 4 -3 18 ]
3 -3 -18
_______________
1 -1 -6 0
The remaining polynomial is x^2 - x - 6 which factors as (x - 3) ( x + 2)
So .... the factored form is (x - 3) ( x - 3) ( x + 2) = ( x + 2) ( x - 3)^2 = 0
Answer:
-11 is correct for all future users.
Step-by-step explanation:
If f(x) = 1x1 + 9 and g(x) = -6, which describes the value of (f + g)(x)?
(f + g)(x) > 3 for all values of x
(f + g)(x) < 3 for all values of x
(f + g)(x) < 6 for all values of x
(f + g)(x) 6 for all values of x
Save and Exit
Ne
Mark this and return
Answer:
The answers are "(f+g)(x)> 3 for all values of x" and "(f+g)(x)<6 for all values of x".
Step-by-step explanation:
If f(x) = 1x1 + 9 =10, then f(x) is a constant for every value of x, which means that y=f(x) will take the value of 10 no matter which value takes x.If g(x)= -6, then g(x) is a constant for every value of x, which means that it will take the value of -6 no matter the value of x.(f+g)(x)=10 + (-6) = 10 - 6= 4. Then, no matter the value of x, the function (f+g)(x) will equal 4 (a constant). According to the available options, both "(f+g)(x)>3" and "(f+g)(x)<6" are true, because (f+g)(x)=4>3 and (f+g)(x)=4 <6.what ordered pairs are a solution to the equations
3x-5y=4
-5x+4y=2
(-7,0)
(6,8)
(3,1)
(-2,-2)
Answer:
x=-2, y=-2. (-2, -2)
Step-by-step explanation:
3x-5y=4
-5x+4y=2
-------------
5(3x-5y)=5(4)
3(-5x+4y)=3(2)
---------------------
15x-25y=20
-15x+12y=6
-------------------
-13y=26
y=26/-13
y=-2
3x-5(-2)=4
3x+10=4
3x=4-10
3x=-6
x=-6/3
x=-2
x=-2, y=-2.
3x minus 7 divided by 2 equals negative 5
Answer: x=0.5
Step-by-step explanation: In order to solve this problem, you need to simplify the rest of the problem first. You can do this by dividing -7 by 2, which will result in -3.5, making the equation 3x-3.5=-5. If you add 3.5 to both sides, the equation becomes 3x = 1.5. If you divide 1.5 by 3, you are left with 0.5, so x=0.5.
Final answer:
The solution to the linear equation '3x minus 7 divided by 2 equals negative 5' is found by performing algebraic operations to isolate the variable, resulting in x = -1.
Explanation:
The question involves solving a linear equation which is a fundamental concept in mathematics. To solve the equation 3x minus 7 divided by 2 equals negative 5, you will perform algebraic operations to isolate the variable x. Here is a step-by-step process:
Multiply both sides of the equation by 2 to get rid of the denominator: 2 * (3x - 7)/2 = -5 * 2.Simplify both sides: 3x - 7 = -10.Add 7 to both sides to isolate the 3x term: 3x = -10 + 7.Simplify the right side: 3x = -3.Divide both sides by 3 to solve for x: x = -3/3.Finally, x simplifies to -1 as the solution.Applying this process, you can see that the original equation is satisfied when x = -1, which completes our solution.
How much grams of cheese do Olivia and sara have together
Answer:
they have 214 grams of cheese together
Answer:
214g
Step-by-step explanation:
Sara has 84 grams of cheese.
Olivia has 130 grams of cheese.
Total amount of cheese = Sara's cheese + Olivia's cheese
Total amount of cheese = 84 + 130
214 = 84 + 130
1. The half-life of the radioactive element krypton-91 is 10 seconds. If 32
grams of krypton - 91 are initially present, how many grams are present
after 30 seconds? Show the decay function. Use A = A0ekt
Answer:
4 g after 30 seconds.
Step-by-step explanation:
After 10 seconds 32 * 1/2 = 16 g are present.
After 20 seconds 32 * (1/2)^2 = 8 g are present
After 30 seconds 32 * (1/2)^3 = 4 g are present.
Ten less than a number is three more than six times the number. Let n represent the number and translate each phase or sentence.
Required number is [tex]\frac{-13}{5}[/tex] and required expression is n – 10 = 6n + 3
Solution:Given that
Ten less than a number is three more than six times the number.
Number is represented by variable "n"
Need to determine equation and the number.
Ten less than number means subtracting 10 from the number
As number is n so ten less than number = n – 10 ------(1)
Six times the number = number multiplied by 6 = 6n
So three more than Six times the number = 6n + 3 --------(2)
As ten less than number is equal to 3 more than six times the number
=> n – 10 = 6n + 3
Solving the above expression for n we get
-10-3 = 6n – n
=> 5n = -13
[tex]\Rightarrow \mathrm{n}=-\frac{13}{5}[/tex]
Hence required number is [tex]-\frac{13}{5}[/tex] and required expression is n – 10 = 6n + 3
Anton has 1 7/8 cups of ice cream to make ice cream sundaes.He uses 2/3 cups of ice cream for each sundae.What is the maximum amount of sundaes that Anton can make with ice cream
Answer:
45/16 or 2 13/16, the maximum amount of sundaes that Anton can make with ice cream is 2.
Step-by-step explanation:
1 7/8=15/8
2/3x<=15/8
x<=(15/8)/(2/3)
x<=(15/8)(3/2)=45/16
Find the slope of the line that goes through the given points.
(3, 5) and (3, -5)
For this case we have that by definition, the slope of a line
is given by:
[tex]m = \frac {y_ {2} -y_{1}} {x_ {2} -x_ {1}}[/tex]
Where:
[tex](x_ {1}, y_ {1})\ and\ (x_ {2}, y_ {2})[/tex] are two points through which the line passes.
According to the statement we have:
[tex](x_ {1}, y_ {1}): (3,5)\\(x_ {2}, y_ {2}): (3, -5)[/tex]
Substituting we have:
[tex]m = \frac {-5-5} {3-3}[/tex]
It is noted that the slope is undefined.
Answer:
The slope is undefined
Find m∠UVT m∠WVU = 169° m∠WVT = (2x + 20)° m∠UVT = (3x + 19)° A) 91° B) 94° C) 97° D) 100°\
Answer:
m ∠ UVT = 97° is the required answer.
Step-by-step explanation:
Given:
m∠WVU = 169°
m∠WVT = (2x + 20)°
m∠UVT = (3x + 19)°
To Find:
m∠UVT = ?
Solution:
Angle Addition Postulate is that if you place two angles side by side, then the measure of the resulting angle will be equal to the sum of the two original angle measures.
So By applying this property in the diagram below we get,
m∠ WVT + m∠UVT = m∠WVU ............{Angle Addition Postulate}
[tex](2x+20) + (3x+19) = 169\\5x + 39 = 169\\5x=169-39\\5x=130\\\therefore x=\frac{130}{5} \\\therefore x=26\\[/tex]
Now,
m∠UVT = (3x + 19)°
Substituting x = 26 we get
m∠UVT = 3 ×26 + 19
= 78 +19
∴ m∠UVT = 97°
From the list below, select the most likely correlation coefficient for the graphed data.
A. −0.1
B. −0.8
C. 0.8
D. 0.1
Answer:
C
Step-by-step explanation:
First of all,
if the line goes Upward (from left to right), it is sloping upward and the correlation coefficient would be POSITIVE.If the line goes Downward (from left to right), it is sloping downward and the correlation coefficient would be NEGATIVE.Since, from the graph we can see that the line is sloping upward, we know the correlation coefficient would be POSITIVE, so we can immediately eliminate choices A & B.
Now, the closer the correlation coefficient value is to 0, the less steep the line is. The closer it is to 1, the more steeper it is.
Looking at the graph, it isn't that flat, it is quite steep. So the correlation coefficient would be 0.8, NOT 0.1
So, answer choice C is right.
45pts help! what is the vertex of the function
f(x)=- -|x + 7| - 4
Answer: (-7, -4)
========================================
Explanation:
The general equation y = a| x-h | + k has the vertex (h,k)
Rewrite the original function in this form to get f(x) = -1|x - (-7)| + (-4) and we see that h = -7 and k = -4
So that's why the vertex is (h,k) = (-7, -4)
The V shape graph opens downward meaning that the vertex (-7, -4) is at the highest point. The graph is shown below. I used GeoGebra to make the graph.
Answer:
-7,-4
Step-by-step explanation:
Find the slope of :
1. (−1, 3) and (5, 4.5)
2. (8.1, −2) and (5.3, −2)
Answer:
General formula of slope=change in y/change in x
1:0.25
2:0
Three friends bought 4, 6, and 8 books. The table shows the cost of the books.
Number of Books 4 6 8
Cost ($) 30 45 60
What is the constant of proportionality?
(A) 2
(B) 7.5
(C) 15
(D) 30
Answer: B 7.5
Step-by-step explanation:
Y = Kx
4 = k30
k = 30/4
k = 7.5
or
Y = KX
X Y
si camilo tiene 6 años mas que juan, juan tiene 7 años menos que andrés y andrés tiene 35 años
¿cuantos años tiene camilo y tiene juan? plantea la ecuación
¿cual es la diferencia entre la edad de camilo y juan?
si la abuela de andres tiene 65 años ¿la suma de las edades de camilo y juan coinciden con la edad de la abuela de andres?
Answer:
Part a) Camilo is 34 years old and Juan is 28 years old
Part b) The difference between Camilo's age and Juan's age is 6 years
Part c) The sum of the ages of Camilo and Juan not coincide with the age of Andres' grandmother
Step-by-step explanation:
The question in English is
If Camilo is 6 years older than Juan, Juan is 7 years younger than Andrés and Andrés is 35 years old .
Part a) How old is Camilo and how old is Juan? raises the equation.
Part b) What's the difference between Camilo's age and Juan's age?
Part c) If Andres's grandmother is 65 years old, does the sum of the ages of Camilo and Juan coincide with the age of Andres' grandmother?
Part a) How old is Camilo and how old is Juan? raises the equation.
Let
x -----> Camilo's age
y -----> Juan's age
z -----> Andres's age
we know that
[tex]x=y+6[/tex] -----> equation A
[tex]y=z-7[/tex] -----> equation B
[tex]z=35[/tex] -----> equation C
Find the value of y
substitute the value of z in the equation B
[tex]y=35-7=28[/tex]
Find the value of x
substitute the value of y in the equation A
[tex]x=28+6=34[/tex]
therefore
Camilo is 34 years old and Juan is 28 years old
Part b) What's the difference between Camilo's age and Juan's age?
Subtract Juan's age from Camilo's age
so
[tex]x-y=34-28=6\ years[/tex]
Part c) If Andres's grandmother is 65 years old, does the sum of the ages of Camilo and Juan coincide with the age of Andres' grandmother?
Adds Camilo's age and Juan's age
[tex]x+y=34+28=62\ years[/tex]
[tex]62\ years\neq 65\ years[/tex]
therefore
The sum of the ages of Camilo and Juan not coincide with the age of Andres' grandmother
Please answer this correctly
Answer:
9:59
Step-by-step explanation:
all you have to do is add the hours to the hours and the minutes to the minutes but if you get a number over 60 in the minutes section then you need to subtract 60 from that side until get a number under 60 then you add however many times you did that to the hours
Answer:
Step-by-step explanation:
9 minutes past 4 = 04:09
Then in 5hours:50minutes, add it to 04:09, then we obtain 09:59
". As an operator in a chemical plant, you tenda
separating machine. After you fill the tank, the
content settles for 14 hours before the liquid is
removed. You fill the tank at 1:45 A.m. When do
you remove the liquid?
A.
2:15 A.M.
B. 2:45 A.M.
C. 3:00 A.M.
D. 3:15 A.M.
E. 3:45 A.M.
Answer:
3:45 P.M.
Step-by-step explanation:
After I fill the tank, the content settles for 14 hours before the liquid is removed.
So, the liquid is removed after content settlement i.e. after 14 hours of filling up the tank.
If I fill the tank at 1:45 A.M. then after 14 hours i.e. at 3: 45 P.M I will remove the liquid.
If we separate the 14 hours into (12 hours + 2 hours), then by adding 12 hours the time will remain the same, only the A.M. will change to P.M i.e. 1: 45 P.M. and then by adding 2 hours more the time will be 3:45 P.M. (Answer)
Are the expressions 4b-7-
2b + 11 and b + 3+ b + 1
equivalent?
Answer:
2b+4 so yes there are equivalent
Step-by-step explanation:
4b-7-2b+11
4b-2b-7+11
2b+4
b+3+b+1
2b+4
Is 12/30 and 18/45 proportional, or not proportional?
12/30 = 18/45, so first you're going to cross multiply and you'll get (30)(18) = (12)(45). Then you can see that 540 = 540 same number so they're proportional...
BTW THIS WAY IS A LOT EASIER.
12/30 = 2/5
18/45 = 2/5
So yes, in summary, they're proportional to each other. Hope this helps, have a BLESSED and wonderful day! :-)
Answer:
proportional
Step-by-step explanation:
12/30 multiplied by a factor of 1.5 is 18/45 so it is proportional
What is a mineral?
a. an element
b. a rock formed from something that was once living
c. a naturally formed solid substance with a crystal structure
Answer:
The answer is definitely C. a naturally formed solid substance with a crystal structure
In the given triangle, ∠AED ∼ ∠ ABC, AD = 6.9, AE = 7.2, DE = 5.2, and BC = 10.2. Find the measure of BD and CE. Round your answer to the nearest tenth.
Answer:
The measure of side BD is 8.6 and The measure of side CE is 8.4
Step-by-step explanation:
Given as :
The Triangle is ABC with side AB , BC , CA
And The points E and D is on the side AB and AC
So, AED is a Triangle
And Δ AED [tex]\sim[/tex] Δ ABC
The measure of side AD = 6.9
The measure of side AE = 7.2
The measure of side ED = 5.2
The measure of side BC = 10.2
Let The The measure of side EB = x
And The measure of side DC = y
So, From similarity property
[tex]\dfrac{AB}{AE}[/tex] = [tex]\dfrac{AC}{AD}[/tex] = [tex]\dfrac{BC}{ED}[/tex]
Or, [tex]\dfrac{AB}{AE}[/tex] = [tex]\dfrac{BC}{ED}[/tex]
So, [tex]\dfrac{7.2 + x}{7.2}[/tex] = [tex]\dfrac{10.2}{5.2}[/tex]
Or, 5.2 × ( 7.2 + x ) = 10.2 × 7.2
Or, 37.44 + 5.2 x = 73.44
Or, 73.44 - 37.44 = 5.2 x
∴ x = [tex]\frac{36}{5.2}[/tex]
I.e x = 6.9
Now in Δ BED
BE² + ED² = BD²
Or, 6.9² + 5.2² = BD²
Or, BD² = 74.65
∴ BD = [tex]\sqrt{74.65}[/tex]
I.e BD = 8.64
Or, BD = 8.6
Similarly for y
[tex]\dfrac{AC}{AD}[/tex] = [tex]\dfrac{BC}{ED}[/tex]
Or, [tex]\dfrac{6.9+y}{6.9}[/tex] = [tex]\dfrac{10.2}{5.2}[/tex]
Or, 5.2 × ( 6.9 + y ) = 10.2 × 6.9
Or, 35.88 + 5.2 y = 70.38
or, 5.2 y = 70.8 - 35.88
Or, 5.2 y = 34.5
∴ y = [tex]\frac{34.5}{5.2}[/tex]
I.e y = 6.6
Now in Δ CED
CD² + ED² = CE²
Or, 6.6² + 5.2² = CE²
Or, CE² = 70.6
∴ CE = [tex]\sqrt{70.6}[/tex]
I.e CE = 8.40
Or, CE = 8.4
Hence The measure of side BD is 8.6 and The measure of side CE is 8.4 Answer
Answer:
By using geometric calculations,the measure of BD and CE are 6.9 and 7.4 respectively.
The function relating the height of an object off the ground to the time spent falling is a quadratic relationship. Travis drops a
tennis ball from the top of an office building 90 meters tall. Three seconds later, the ball lands on the ground. After 2
seconds, how far is the ball off the ground?
Answer:
the ball is on the ground after 3 seconds right so it would still be on the ground
Step-by-step explanation:
Answer:50 meters
Step-by-step explanation:
Okay, how many weeks would you have to work to pay for Gary's $1200 mistake?
The number of weeks requires is 15 weeks
What is Unitary method?It is a method where we find the value of a single unit from the value of multiple units and the value of multiple units from the value of a single unit.
Steps to Use Unitary Method
First, let us make a note of the information we have. There are 5 ice-creams. 5 ice-creams cost $125.
Step 1: Let’s find the cost of 1 ice cream. In order to do that, divide the total cost of ice-creams by the total number of ice-creams. The cost of 1 ice-cream = Total cost of ice-creams/Total number of ice-creams = 125/5 = 25. Therefore, the cost of 1 ice cream is $25.
Step 2: To find the cost of 3 ice-creams, multiply the cost of 1 ice cream by the number of ice-creams. The cost of 3 ice-creams is cost of 1 ice-cream × number of ice-creams = 25 × 3 = $75. Finally, we have the cost of 3 ice-creams i.e. $75.
Given:
$85.00 a week just from Allowance
So, Gary have to work
=1200/85
= 15 weeks
Hence, the number of weeks requires is 15 weeks.
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The complete question is
can someone help me please?
Question : If you have a job or allowance, how much do you take home per week?
I put that I make $85.00 a week just from Allowance and my half job.
So the question is : how many weeks would you have to work to pay for Gary's $1200 mistake?
[calculate $1200 � your take home pay amount = answer in weeks]
Weeks for Laptop:
how many weeks would you have to work to pay for your little mistake with the $13 bounced check? You know, that $4300 messup? Weeks for pizza :
Help please thanks
Final answer:
Jason will have to work approximately 6.67 weeks, or about 6 weeks and 5 days, to pay off a $1200 mistake if he earns $4.50 per hour after government income reduction.
Explanation:
To calculate how many weeks a student would have to work to pay for a $1200 mistake, we will use the information provided about Jason's income and work scenario as a reference. According to the information, Jason nets $4.50 for every hour of work due to a reduction in government income. Thus, if Jason has to repay $1200, we will divide this amount by his net hourly income to find the total hours he needs to work.
$1200 ÷ $4.50 per hour = 266.67 hours
Now, to convert these hours into weeks, we assume a standard work week is 40 hours. Therefore, we divide the total hours by 40 hours per week.
266.67 hours ÷ 40 hours per week = 6.67 weeks
Jason will have to work approximately 6.67 weeks to pay off a $1200 mistake.
AP:2,x,26.
Find the value of x
2,x, 26 are in A. P.
a2-a1 = a3-a2
x-2 = 26-x
2x = 26+2
2x = 28
So x = 14.